You might try some Akamai resellers? I don't know if Akamai resellers always have the full Akamai feature set or not. But it's likely that you can get a better deal on Akamai at low commit volumes from resellers (it is common for large CDNs to not deal with small customers directly, but let small customers be handled by resellers).

I don't know which other CDNs have ESI -- ESI was AFAIK created by Akamai, so it's a fair guess that they might have the most comprehensive support for it.

Additionally, I know that Rackspace's Cloud Files CDN is Akamai now -- but with Rackspace I don't believe you get access to Akamai's own management UI, you only get Rackspace's very limited UI. And from this you cannot configure ESI. But perhaps Rackspace's support people can set up ESI for you, try contacting them on their support chat.

Best of luck, and please, report back here if you find a good solution to this! :-)